What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 8001 | 2^335468-18629 | 100986 | Enzo Doria | 05/2013 |
| 8002 | 2^335454-20961 | 100982 | Enzo Doria | 06/2013 |
| 8003 | (2^335454+3258)/2 | 100982 | Stefano Morozzi | 02/2021 |
| 8004 | 10^100978+61 | 100979 | Lelio R Paula | 09/2016 |
| 8005 | 10^100978-156437 | 100978 | Patrick De Geest | 11/2016 |
| 8006 | (2^335422+3114)/2 | 100972 | Stefano Morozzi | 09/2020 |
| 8007 | (35*10^100970-89)/9 | 100971 | Robert Price | 02/2022 |
| 8008 | (15*2^335417+1)/481 | 100970 | Lelio R Paula | 12/2013 |
| 8009 | 2^335403-1859167 | 100967 | Enzo Doria | 03/2016 |
| 8010 | 23599^18976+18976^23599 | 100962 | Hans Havermann | 10/2018 |
| 8011 | 6*10^100958+43 | 100959 | Robert Price | 07/2020 |
| 8012 | 9*2^335364-5 | 100956 | Lelio R Paula | 08/2014 |
| 8013 | (7998^25867-1)/7997 | 100955 | Serge Batalov | 06/2022 |
| 8014 | 2^335349+72287 | 100951 | Enzo Doria | 04/2016 |
| 8015 | 2^335329+16095 | 100945 | Lelio R Paula | 09/2016 |
| 8016 | 232823#+233663 | 100937 | Makoto Morimoto | 10/2017 |
| 8017 | (232823#+10141)/(10141*1674461) | 100927 | Makoto Morimoto | 06/2019 |
| 8018 | 2^335237-20893 | 100917 | Enzo Doria | 06/2013 |
| 8019 | 2^335222-19337 | 100912 | Enzo Doria | 05/2013 |
| 8020 | 2^335222-109985 | 100912 | Enzo Doria | 04/2014 |
| 8021 | 2^335182-17237 | 100900 | Enzo Doria | 05/2013 |
| 8022 | (2^335107+1634)/2 | 100877 | Stefano Morozzi | 09/2020 |
| 8023 | 2^335043-16737 | 100858 | Enzo Doria | 05/2013 |
| 8024 | (21181*2^335049+1)/1343811 | 100858 | Lelio R Paula | 07/2014 |
| 8025 | 2^335038-20633 | 100857 | Enzo Doria | 06/2013 |
| 8026 | 2^335031+1873373 | 100855 | Enzo Doria | 06/2016 |
| 8027 | 23489^19650+19650^23489 | 100847 | Hans Havermann | 10/2018 |
| 8028 | 3^211354-8816 | 100842 | Enzo Doria | 05/2014 |
| 8029 | 2^334984-112757 | 100841 | Enzo Doria | 06/2014 |
| 8030 | (746*10^100827+1)/9 | 100829 | Robert Price | 03/2020 |
| 8031 | 29451^2648+2648^29451 | 100809 | Hans Havermann | 09/2018 |
| 8032 | 25583^8716+8716^25583 | 100806 | Hans Havermann | 08/2018 |
| 8034 | 2^334857+48527 | 100803 | Lelio R Paula | 08/2011 |
| 8033 | 12^93406+29 | 100803 | Lelio R Paula | 10/2016 |
| 8035 | 28780^3179+3179^28780 | 100796 | Hans Havermann | 09/2018 |
| 8036 | (5*2^334825+1)/47 | 100792 | Lelio R Paula | 12/2013 |
| 8037 | (328^40063-1)/327 | 100791 | Serge Batalov | 06/2022 |
| 8038 | 2^334809-13 | 100788 | Lelio R Paula | 04/2011 |
| 8039 | (3552^28387-1)/3551 | 100784 | Serge Batalov | 06/2022 |
| 8040 | (82*10^100780-1)/9 | 100781 | Robert Price | 12/2014 |
| 8041 | 31395^1622+1622^31395 | 100780 | Hans Havermann | 09/2018 |
| 8042 | (2^334779+47)/5 | 100778 | Lelio R Paula | 12/2013 |
| 8043 | 2^334751+2049 | 100771 | Lelio R Paula | 09/2016 |
| 8044 | 13^90443-98 | 100749 | Lelio R Paula | 10/2016 |
| 8045 | (2^334674+3190)/2 | 100747 | Stefano Morozzi | 09/2020 |
| 8046 | (2^334651+1050)/2 | 100740 | Stefano Morozzi | 09/2020 |
| 8047 | (7*10^100737+71)/3 | 100738 | Robert Price | 05/2018 |
| 8048 | (24737*2^334628+1)/3 | 100737 | Lelio R Paula | 07/2014 |
| 8049 | 15^85639-28 | 100720 | Lelio R Paula | 10/2016 |
| 8050 | 27068^5259+5259^27068 | 100718 | Hans Havermann | 08/2018 |
| 8051 | 2^334562+577294575 | 100711 | Lelio R Paula | 09/2016 |
| 8052 | 4*3^211077-5 | 100710 | Lelio R Paula | 08/2014 |
| 8053 | 2^334524+145 | 100702 | Lelio R Paula | 07/2009 |
| 8054 | (2^334451+714)/2 | 100680 | Stefano Morozzi | 09/2020 |
| 8055 | 27648^4375+4375^27648 | 100666 | Hans Havermann | 09/2018 |
| 8056 | (1017*2^334391-1)/3535 | 100662 | Lelio R Paula | 05/2015 |
| 8057 | (2^334309+3122)/2 | 100637 | Stefano Morozzi | 09/2020 |
| 8058 | 2^334294-113111 | 100633 | Enzo Doria | 07/2014 |
| 8059 | 25581^8582+8582^25581 | 100626 | Hans Havermann | 08/2018 |
| 8061 | 6^129308-17723 | 100622 | Enzo Doria | 03/2013 |
| 8060 | (19*10^100627+287)/9/292157 | 100622 | Alfred Reich | 11/2022 |
| 8062 | 6^129305+95 | 100619 | Lelio R Paula | 10/2016 |
| 8063 | 2^334244-1167 | 100618 | Lelio R Paula | 09/2016 |
| 8064 | (2^334233+3066)/2 | 100614 | Stefano Morozzi | 09/2020 |
| 8065 | (76*10^100611+77)/9 | 100612 | Robert Price | 10/2019 |
| 8066 | 7*10^100606-93 | 100607 | Robert Price | 08/2020 |
| 8067 | (26*10^100566+49)/3 | 100567 | Robert Price | 08/2019 |
| 8068 | (21*2^334050+1)/935 | 100558 | Lelio R Paula | 12/2013 |
| 8069 | 24885^10984+10984^24885 | 100555 | Hans Havermann | 07/2018 |
| 8070 | (1351^32119-1)/1350 | 100551 | Serge Batalov | 06/2022 |
| 8071 | (78557*2^334018+1)/4326021 | 100548 | Lelio R Paula | 07/2014 |
| 8072 | (35*10^100542+1)/9 | 100543 | Serge Batalov | 11/2010 |
| 8073 | 23578^18367+18367^23578 | 100538 | Hans Havermann | 07/2018 |
| 8074 | 13^90251+24 | 100535 | Lelio R Paula | 10/2016 |
| 8075 | 2^333963+789 | 100533 | Lelio R Paula | 08/2011 |
| 8076 | 2^333919-1840087 | 100520 | Enzo Doria | 06/2015 |
| 8077 | (2^333916+1698)/2 | 100519 | Stefano Morozzi | 09/2020 |
| 8078 | 2^333911+72623 | 100518 | Enzo Doria | 04/2016 |
| 8079 | 24605^12168+12168^24605 | 100517 | Hans Havermann | 08/2018 |
| 8080 | 66*10^100502+7 | 100504 | Robert Price | 07/2020 |
| 8081 | 18^80064-67 | 100503 | Lelio R Paula | 10/2016 |
| 8082 | (13*10^100487+137)/3 | 100488 | Robert Price | 06/2021 |
| 8083 | 5^143742-48 | 100472 | Lelio R Paula | 10/2016 |
| 8084 | 24095^14784+14784^24095 | 100472 | Hans Havermann | 08/2018 |
| 8085 | 2^333757-112123 | 100471 | Enzo Doria | 06/2014 |
| 8086 | (7953^25759-1)/7952 | 100470 | Serge Batalov | 06/2022 |
| 8087 | 7*10^100457-57 | 100458 | Robert Price | 06/2020 |
| 8088 | 27358^4693+4693^27358 | 100444 | Hans Havermann | 07/2018 |
| 8089 | 8*10^100439-51 | 100440 | Robert Price | 08/2019 |
| 8090 | 2^333603-108861 | 100425 | Enzo Doria | 03/2014 |
| 8091 | 9*7^118818-2 | 100414 | Lelio R Paula | 11/2014 |
| 8092 | 2^333546-17097 | 100408 | Enzo Doria | 05/2013 |
| 8093 | (19*10^100403+287)/9/3 | 100403 | Alfred Reich | 11/2022 |
| 8094 | 17^81597+72 | 100401 | Lelio R Paula | 10/2016 |
| 8095 | (3613^28219-1)/3612 | 100396 | Serge Batalov | 06/2022 |
| 8096 | p(20559)#/2+8 | 100384 | Robert Price | 01/2017 |
| 8097 | 11^96390-24 | 100380 | Lelio R Paula | 10/2016 |
| 8098 | (2^333385+2730)/2 | 100359 | Stefano Morozzi | 09/2020 |
| 8099 | 4832563059*2^333333+30029 | 100353 | Donovan Johnson | 01/2008 |
| 8100 | 23565^18136+18136^23565 | 100353 | Hans Havermann | 07/2018 |
| 8101 | 2^333354+763 | 100350 | Lelio R Paula | 08/2011 |
| 8102 | (1608961*2^333333+1)/3 | 100349 | Alex_soldier | 09/2022 |
| 8103 | (424517*2^333333+1)/5 | 100349 | Alex_soldier | 09/2022 |
| 8104 | (887087*2^333333+1)/5 | 100349 | Alex_soldier | 09/2022 |
| 8105 | (1159703*2^333333+1)/7 | 100349 | Alex_soldier | 09/2022 |
| 8106 | (25*10^100343-67)/3 | 100344 | Robert Price | 06/2019 |
| 8107 | 2^333289-109483 | 100330 | Enzo Doria | 04/2014 |
| 8108 | 2^333240-2790209 | 100316 | Enzo Doria | 03/2016 |
| 8109 | 23601^17798+17798^23601 | 100314 | Hans Havermann | 05/2018 |
| 8111 | (2^333227-2^166614+1)/5 | 100311 | | 11/2006 |
| 8110 | 2^333225+719 | 100311 | Lelio R Paula | 08/2011 |
| 8112 | 2^333221-2785333 | 100310 | Enzo Doria | 10/2015 |
| 8113 | 76^53332-75 | 100308 | Norbert Schneider | 02/2015 |
| 8114 | (29*10^100302+583)/9 | 100303 | Robert Price | 06/2021 |
| 8115 | 6^128892-17573 | 100298 | Enzo Doria | 03/2013 |
| 8116 | (47*10^100283-119)/9 | 100284 | Robert Price | 05/2019 |
| 8117 | 2^333105-113215 | 100275 | Enzo Doria | 07/2014 |
| 8118 | (31*2^333102+1)/2375 | 100272 | Lelio R Paula | 11/2013 |
| 8119 | 4*10^100257-83 | 100258 | Robert Price | 10/2018 |
| 8120 | 17^81476-74 | 100253 | Lelio R Paula | 10/2016 |
| 8121 | 23392^19207+19207^23392 | 100199 | Hans Havermann | 06/2018 |
| 8122 | (2^332830+750)/2 | 100192 | Stefano Morozzi | 09/2020 |
| 8123 | (206*10^100189-17)/9 | 100191 | Robert Price | 01/2020 |
| 8124 | 17^81417-16 | 100180 | Theodore Burton | 11/2005 |
| 8125 | (2^332773+590)/2 | 100175 | Stefano Morozzi | 09/2020 |
| 8126 | 2^332739-113215 | 100165 | Enzo Doria | 07/2014 |
| 8127 | 2^332730-1865621 | 100162 | Enzo Doria | 03/2016 |
| 8128 | 91^51127-2 | 100160 | Lelio R Paula | 09/2013 |
| 8129 | 15^85159-32 | 100155 | Lelio R Paula | 10/2016 |
| 8130 | 6^128661+97 | 100118 | Lelio R Paula | 10/2016 |
| 8131 | 19^78285+40 | 100108 | Lelio R Paula | 07/2016 |
| 8132 | 6^128640+5 | 100102 | Lelio R Paula | 11/2014 |
| 8133 | 10^100095+89973 | 100096 | Patrick De Geest | 10/2022 |
| 8134 | 10^100095-400001 | 100095 | Robert Price | 09/2021 |
| 8135 | 10^100095-203693 | 100095 | Patrick De Geest | 10/2022 |
| 8136 | 22779^22970-22970^22779 | 100093 | Norbert Schneider | 08/2020 |
| 8137 | (2^332468+3130)/2 | 100083 | Stefano Morozzi | 09/2020 |
| 8138 | (14*10^100075+61)/3 | 100076 | Robert Price | 12/2018 |
| 8139 | (2^332435+3098)/2 | 100073 | Stefano Morozzi | 09/2020 |
| 8140 | 28562^3189+3189^28562 | 100072 | Hans Havermann | 05/2018 |
| 8141 | 6^128565-127 | 100044 | Lelio R Paula | 08/2016 |
| 8142 | (2^332317+2106)/2 | 100038 | Stefano Morozzi | 09/2020 |
| 8144 | 2^332309-133 | 100035 | Lelio R Paula | 02/2011 |
| 8145 | 2^332307+731 | 100035 | Lelio R Paula | 07/2011 |
| 8143 | 937^33662-33662^937 | 100035 | Norbert Schneider | 05/2023 |
| 8146 | 2^332301+12927 | 100033 | Lelio R Paula | 04/2013 |
| 8147 | 23406^18781+18781^23406 | 100031 | Hans Havermann | 04/2018 |
| 8148 | 2^332277-4573 | 100026 | Yves Minet | 03/2019 |
| 8149 | 12^92684-13 | 100023 | Lelio R Paula | 07/2016 |
| 8150 | 70^54207-54207^70 | 100018 | Norbert Schneider | 04/2023 |
| 8151 | 78557*2^332193+55669 | 100005 | Jorge Menendez | 04/2019 |
| 8152 | 78557*2^332192+72689 | 100005 | Jorge Menendez | 04/2019 |
| 8153 | 10^100003+45799 | 100004 | Stefano Morozzi | 04/2019 |
| 8154 | 10^100003+155461 | 100004 | Stefano Morozzi | 04/2019 |
| 8155 | 10^100003+211389 | 100004 | Stefano Morozzi | 04/2019 |
| 8156 | 10^100003+381027 | 100004 | Stefano Morozzi | 04/2019 |
| 8157 | 10^100003+540703 | 100004 | Stefano Morozzi | 04/2019 |
| 8158 | 10^100003+823977 | 100004 | Stefano Morozzi | 04/2019 |
| 8170 | 10^100002+236023 | 100003 | Stefano Morozzi | 05/2018 |
| 8171 | 10^100002+433741 | 100003 | Stefano Morozzi | 05/2018 |
| 8159 | 2^332202+104659 | 100003 | Stefano Morozzi | 04/2019 |
| 8160 | 2^332202+857539 | 100003 | Stefano Morozzi | 04/2019 |
| 8161 | 2^332202+181773 | 100003 | Stefano Morozzi | 04/2019 |
| 8162 | 2^332202+687543 | 100003 | Stefano Morozzi | 04/2019 |
| 8163 | 2^332202+941595 | 100003 | Stefano Morozzi | 04/2019 |
| 8164 | 2^332202+445813 | 100003 | Stefano Morozzi | 04/2019 |
| 8165 | 2^332202+1599727 | 100003 | Stefano Morozzi | 04/2019 |
| 8166 | 2^332202+1389567 | 100003 | Stefano Morozzi | 04/2019 |
| 8167 | 2^332202+1206315 | 100003 | Stefano Morozzi | 04/2019 |
| 8168 | 2^332202+1958647 | 100003 | Stefano Morozzi | 04/2019 |
| 8169 | 10^100003-562857 | 100003 | Patrick De Geest | 07/2019 |
| 8172 | (10^100002-1)/9-10^33441 | 100002 | Akihiko Yoshida | 03/2018 |
| 8173 | (10^100002-1)/9-10^44692 | 100002 | Akihiko Yoshida | 03/2018 |
| 8174 | 10^100002-249519 | 100002 | Patrick De Geest | 07/2018 |
| 8175 | 10^100001+314199 | 100002 | Patrick De Geest | 07/2018 |
| 8195 | 10^100000+3938473 | 100001 | Robert Price | 05/2015 |
| 8196 | 10^100000+3979761 | 100001 | Robert Price | 05/2015 |
| 8197 | 10^100000+4293973 | 100001 | Robert Price | 09/2015 |
| 8192 | 10^100000+4858267 | 100001 | Robert Price | 12/2015 |
| 8193 | 10^100000+5113299 | 100001 | Robert Price | 02/2016 |
| 8194 | 10^100000+5169411 | 100001 | Robert Price | 02/2016 |
| 8184 | 10^100000+5354043 | 100001 | Robert Price | 05/2016 |
| 8185 | 10^100000+5717979 | 100001 | Robert Price | 05/2016 |
| 8186 | 10^100000+6080631 | 100001 | Robert Price | 07/2016 |
| 8187 | 10^100000+6308469 | 100001 | Robert Price | 07/2016 |
| 8188 | 10^100000+6512023 | 100001 | Robert Price | 08/2016 |
| 8189 | 10^100000+6596557 | 100001 | Robert Price | 08/2016 |
| 8190 | 10^100000+7115409 | 100001 | Robert Price | 10/2016 |
| 8191 | 10^100000+7235803 | 100001 | Robert Price | 10/2016 |
| 8198 | 10^100000+7867333 | 100001 | Robert Price | 12/2016 |
| 8199 | 10^100000+8743093 | 100001 | Robert Price | 02/2017 |
| 8200 | 10^100000+8955391 | 100001 | Robert Price | 03/2017 |
| 8201 | 10^100000+9180019 | 100001 | Robert Price | 03/2017 |
| 8202 | 10^100000+9225987 | 100001 | Robert Price | 04/2017 |
| 8203 | 10^100000+9265587 | 100001 | Robert Price | 04/2017 |
| 8204 | 10^100000+9287049 | 100001 | Robert Price | 04/2017 |
| 8205 | 10^100000+9425053 | 100001 | Robert Price | 05/2017 |
| 8206 | 10^100000+9450769 | 100001 | Robert Price | 05/2017 |
| 8207 | 10^100000+9528747 | 100001 | Robert Smith | 05/2017 |
| 8208 | 10^100000+9548071 | 100001 | Robert Price | 06/2017 |
| 8209 | 10^100000+10064287 | 100001 | Robert Price | 08/2017 |
| 8210 | 10^100000+10229569 | 100001 | Robert Price | 10/2017 |
| 8176 | 10^100000+11187931 | 100001 | Robert Price | 03/2018 |
| 8177 | 10^100000+11264721 | 100001 | Robert Price | 04/2018 |
| 8178 | 10^100000+11477661 | 100001 | Robert Price | 05/2018 |
| 8179 | 10^100000+11644653 | 100001 | Robert Price | 07/2018 |
| 8180 | 10^100001-431439 | 100001 | Patrick De Geest | 07/2018 |
| 8181 | 10^100000+11769399 | 100001 | Robert Price | 08/2018 |
| 8182 | 10^100000+11848159 | 100001 | Robert Price | 08/2018 |
| 8183 | 10^100000+11863467 | 100001 | Robert Price | 08/2018 |
| 8211 | 10^100000+11992051 | 100001 | Robert Price | 09/2018 |
| 8212 | 2^332196-1-2*29696 | 100001 | Matt Stath | 11/2018 |
| 8213 | 10^100000+12363957 | 100001 | Robert Price | 11/2018 |
| 8214 | 2^332196+1+2*17152 | 100001 | Matt Stath | 12/2018 |
| 8215 | 10^100000+12778033 | 100001 | Robert Price | 02/2019 |
| 8216 | 10^100000+13581679 | 100001 | Robert Price | 05/2019 |
| 8217 | 10^100000+13613199 | 100001 | Robert Price | 05/2019 |
| 8218 | 10^100000+13752327 | 100001 | Robert Price | 05/2019 |
| 8219 | 10^100000+14139243 | 100001 | Robert Price | 06/2019 |
| 8220 | 10^100000+14151057 | 100001 | Robert Price | 06/2019 |
| 8221 | 10^100000+14218923 | 100001 | Robert Price | 06/2019 |
| 8222 | 10^100000+24543147 | 100001 | Robert Price | 08/2021 |
| 8223 | 10^100000+24781659 | 100001 | Robert Price | 08/2021 |
| 8224 | 10^100000+24906153 | 100001 | Robert Price | 08/2021 |
| 8225 | 10^100000+25682679 | 100001 | Robert Price | 10/2021 |
| 8226 | 10^100000+25905301 | 100001 | Robert Price | 10/2021 |
| 8227 | 10^100000+25923967 | 100001 | Robert Price | 10/2021 |
| 8228 | 10^100000+26061691 | 100001 | Robert Price | 10/2021 |
| 8229 | 10^100000+26173351 | 100001 | Robert Price | 11/2021 |
| 8230 | 10^100000+26673487 | 100001 | Robert Price | 11/2021 |
| 8231 | 10^100000+26849359 | 100001 | Robert Price | 12/2021 |
| 8232 | 10^100000+26893887 | 100001 | Robert Price | 12/2021 |
| 8233 | 10^100000+26954551 | 100001 | Robert Price | 12/2021 |
| 8234 | 10^100000+27024543 | 100001 | Robert Price | 12/2021 |
| 8235 | 10^100000+27060877 | 100001 | Robert Price | 12/2021 |
| 8236 | 10^100000+27617577 | 100001 | Robert Price | 03/2022 |
| 8237 | 10^100000+27869671 | 100001 | Robert Price | 03/2022 |
| 8238 | 10^100000+27956481 | 100001 | Robert Price | 03/2022 |
| 8239 | 10^100000+28078261 | 100001 | Robert Price | 03/2022 |
| 8240 | 10^100000+28150203 | 100001 | Robert Price | 03/2022 |
| 8241 | 10^100000+28626021 | 100001 | Robert Price | 05/2022 |
| 8242 | 10^100000+28649299 | 100001 | Robert Price | 05/2022 |
| 8243 | 10^100000+29409799 | 100001 | Robert Price | 06/2022 |
| 8244 | 10^100000+29415577 | 100001 | Robert Price | 06/2022 |
| 8245 | 10^100000+29424201 | 100001 | Robert Price | 06/2022 |
| 8246 | 10^100000+29610153 | 100001 | Robert Price | 07/2022 |
| 8247 | 10^100000+30166789 | 100001 | Robert Price | 07/2022 |
| 8248 | 10^100000+30338259 | 100001 | Robert Price | 07/2022 |
| 8249 | 10^100000+30540031 | 100001 | Robert Price | 07/2022 |
| 8250 | 10^100000+30635157 | 100001 | Robert Price | 07/2022 |
